Problem: ${4 \div \dfrac{2}{9} =}$
Explanation: $4 \div \dfrac{2}{9}} ={\dfrac41} \div \dfrac{2}{9}} $ $~~~~~~~{\gray{\text{Rewrite 4 as }\dfrac41.}} $ $\phantom{4 \div \dfrac{2}{3}}} ={\dfrac41} \times \dfrac{9}{2}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac29.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{4\timesD9}{1\timesD2}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{36}{2}} $ $~~~~~~~{\gray{\text{Simplify. }}} $ $\phantom{8 \div \dfrac{2}{3}}} =18 $ ${4 \div \dfrac{2}{9} =18}$